In my tests so far, HyperResearch 4.0 runs nearly flawlessly in Linux.
First, install HyperResearch, then install Quicktime in order to edit and play video files.
Problem found.
HyperResearch will crash if you switch to another
application that is also running in WINE and then click on the menu bar
to try to return to HyperRESEARCH.
Workaround.
When returning to HyperRESEARCH, avoid clicking on the
menu bar. Instead, try to un-minimize or show any of the main windows
(Study, Code Book, etc.) and click on the title bar of the window you
want to work with, or any window, to make it active, before clicking on
the menu bar. This should avoid the crash.